Respuesta :
Answer:
The correct option is (A).
Step-by-step explanation:
The multiple linear regression equation is given by, [tex]y=\alpha +\beta _{1} x_{1}+\beta _{2}x_{2}[/tex], where α = constant and β[tex]_{i}[/tex] = slope coefficients of regression line.
To test if there is a important relationship amid X[tex]_{i}[/tex] and Y, we use the t-statistic test.
The t-statistic for regression coefficient analysis is given by,
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
The regression equation for test scores dependent upon the two explanatory variables, the student-teacher ratio and the percent of English learners is:
[tex]\text{TestScore} = 698.9 - 1.10 \text{ STR} - 0.650 \text{ PctEL}[/tex]
A t-test for the significance of the regression coefficient of variable student-teacher ratio (STR) is conducted.
The test statistic is found to be, t = 2.56.
The regression coefficient of variable STR is, 1.10.
Compute the standard error of the regression coefficient as follows:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
[tex]S.E._{\beta_{i}}=\frac{\beta_{i}}{t}[/tex]
[tex]=\frac{1.10}{2.56}\\\\=0.4296875\\\\\approx 0.43[/tex]
The standard error of the regression coefficient is 0.43.
Thus, the correct option is (A).
